The entropies of renewal systems

Abstract

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX W ⊂A Z formed by bi-infinite concatenations of words fromW. Motivated by Adler's question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems.

Date of Award	1991
Original language	American English
Awarding Institution	Tel Aviv University
Supervisor	Meir Smorodinsky (Supervisor)